Next-to-next-to-leading order O(αs4){\cal O}(\alpha_s^4) results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions

We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.Comment: 12 pages, 2 figures, electronic results file, abbreviation NNLO in Title and Abstract expanded, Summary expanded, reference updated, version to appear in Phys.Rev.

One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up to O(epsilon^2)

We present complete analytical ${\mathcal O}(\epsilon^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.Comment: 25 pages, 6 figures in the text, Revtex, one reference added, minor improvements in the text, to appear in Phys.Rev.

15 years of comet photometry: A comparative analysis of 80 comets

In 1976 we began a program of narrowband photometry of comets that has encompassed well over 400 nights of observations. To date, the program has provided detailed information on 80 comets, 11 of which have been observed on multiple apparitions. In this paper we present the observed range of compositions (molecular production rate ratios) and dustiness (gas production compared with AF-rho) for a well sampled group of comets. Based on these results we present preliminary analysis of taxonomic groupings as well as the abundance ratios we associate with a 'typical' comet

Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

Water Ice and Dust in the Innermost Coma of Comet 103P/Hartley 2

On November 4th, 2010, the Deep Impact eXtended Investigation (DIXI) successfully encountered comet 103P/Hartley 2, when it was at a heliocentric distance of 1.06 AU. Spatially resolved near-IR spectra of comet Hartley 2 were acquired in the 1.05-4.83 micron wavelength range using the HRI-IR spectrometer. We present spectral maps of the inner ~10 kilometers of the coma collected 7 minutes and 23 minutes after closest approach. The extracted reflectance spectra include well-defined absorption bands near 1.5, 2.0, and 3.0 micron consistent in position, bandwidth, and shape with the presence of water ice grains. Using Hapke's radiative transfer model, we characterize the type of mixing (areal vs. intimate), relative abundance, grain size, and spatial distribution of water ice and refractories. Our modeling suggests that the dust, which dominates the innermost coma of Hartley 2 and is at a temperature of 300K, is thermally and physically decoupled from the fine-grained water ice particles, which are on the order of 1 micron in size. The strong correlation between the water ice, dust, and CO2 spatial distribution supports the concept that CO2 gas drags the water ice and dust grains from the nucleus. Once in the coma, the water ice begins subliming while the dust is in a constant outflow. The derived water ice scale-length is compatible with the lifetimes expected for 1-micron pure water ice grains at 1 AU, if velocities are near 0.5 m/s. Such velocities, about three order of magnitudes lower than the expansion velocities expected for isolated 1-micron water ice particles [Hanner, 1981; Whipple, 1951], suggest that the observed water ice grains are likely aggregates.Comment: 51 pages, 12 figures, accepted for publication in Icaru

G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those already known). We find four families of solutions, each one containing arbitrary parameters for which no differential equations remain to be integrated. We write the line-elements in a simplified form and perform a detailed study for each of these solutions, giving the kinematical quantities of the fluid velocity vector, the energy-density and pressure, values of the parameters for which the energy conditions are fulfilled everywhere, the Petrov type, the singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker metrics contained in each family.Comment: Latex, no figure

On the Symmetries of the Edgar-Ludwig Metric

The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected fifteen independent conformal Killing vectors exist, but in general the metric admits no Killing or homothetic vectors. However for certain special cases a one-dimensional group of homotheties or motions may exist and in one very special case, overlooked by previous investigators, a two-dimensional homethety group exists. No higher dimensional groups of motions or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure

Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms

Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku, and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can only be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al. and Baekler et al., emerges also in the framework of Diakonov et al.(2011). We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann-Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) Only in a Riemann-Cartan spacetime, that is, in a spacetime with torsion, parity violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann-Cartan spacetime is a natural habitat for chiral fermionic matter fields.Comment: 12 page latex, as version 2 an old file was submitted by mistake, this is now the real corrected fil

Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part

We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$ and the curvature pseudo-scalar $X$ linearly and quadratically (including an $RX$ term) and (ii) pieces quadratic in the torsion {\it vector} $\cal V$ and the torsion {\it axial} vector $\cal A$ (including a ${\cal V}{\cal A}$ term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms (`world') and of parity violating terms (`shadow world'). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic `torsion cosmologies' of Shie-Nester-Yo (2008) and Chen et al.\ (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces $R(t)$ and $X(t)$. Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.Comment: Latex computerscript, 25 pages; mistakes corrected, references added, notation and title slightly changed; accepted by Phys. Rev.

Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra